Convex space

In mathematics, a convex space (or barycentric algebra) is a space in which it is possible to take convex combinations of any sets of points.

[1][2] A convex space can be defined as a set

equipped with a binary convex combination operation

satisfying: From this, it is possible to define an n-ary convex combination operation, parametrised by an n-tuple

More generally, any convex subset of a real affine space is a convex space.

Convex spaces have been independently invented many times and given different names, dating back at least to Stone (1949).